We present a compact, deployable heart rate (HR) estimation system using photoplethysmography (PPG) and inertial measurement unit (IMU) data, combining TimeWeaver, a conditional diffusion model for metadata-aware synthetic augmentation, with progressive structured pruning of Temporal Convolutional Networks (TCNs). Our smallest model, with 1.56k parameters, achieves a mean absolute error (MAE) of 4.92 BPM on the PPG-DaLiA dataset and supports real-time inference ($<{40 ms}$latency) on a 64 MHz ARM Cortex-M4F microcontroller (MCU) without requiring quantization. Synthetic data conditioned on subject metadata, HR, and activity type significantly enhances model generalization, enabling pruned models to match or exceed the accuracy of larger baselines, achieving over a 23% improvement compared to training on real data alone. Our work establishes a new Pareto frontier for real-time, on-device HR monitoring using diffusion-augmented training and sub-2 k parameter models.

Generating realistic time series samples is crucial for stress-testing models and protecting user privacy by using synthetic data. In engineering and safety-critical applications, these samples must meet certain hard constraints that are domain-specific or naturally imposed by physics or nature. Consider, for example, generating electricity demand patterns with constraints on peak demand times. This can be used to stress-test the functioning of power grids during adverse weather conditions. Existing approaches for generating constrained time series are either not scalable or degrade sample quality. To address these challenges, we introduce Constrained Posterior Sampling (CPS), a diffusion-based sampling algorithm that aims to project the posterior mean estimate into the constraint set after each denoising update. Notably, CPS scales to a large number of constraints ($\sim100$) without requiring additional training. We provide theoretical justifications highlighting the impact of our projection step on sampling. Empirically, CPS outperforms state-of-the-art methods in sample quality and similarity to real time series by around 70\% and 22\%, respectively, on real-world stocks, traffic, and air quality datasets.

Imagine generating a city’s electricity demand pattern based on weather, the presence of an electric vehicle, and location, which could be used for capacity planning during a winter freeze. Such real-world time series are often enriched with paired heterogeneous contextual metadata (e.g., weather and location). Current approaches to time series generation often ignore this paired metadata. Additionally, the heterogeneity in metadata poses several practical challenges in adapting existing conditional generation approaches from the image, audio, and video domains to the time series domain. To address this gap, we introduce TIME WEAVER, a novel diffusion-based model that leverages the heterogeneous metadata in the form of categorical, continuous, and even time-variant variables to significantly improve time series generation. Additionally, we show that naive extensions of standard evaluation metrics from the image to the time series domain are insufficient. These metrics do not penalize conditional generation approaches for their poor specificity in reproducing the metadata-specific features in the generated time series. Thus, we innovate a novel evaluation metric that accurately captures the specificity of conditional generation and the realism of the generated time series. We show that TIME WEAVER outperforms state-of-the-art benchmarks, such as Generative Adversarial Networks (GANs), by up to 30% in downstream classification tasks on real-world energy, medical, air quality, and traffic datasets.